To solve for $x$ in this right triangle, we can apply the Pythagorean Theorem. The Pythagorean Theorem states that in any right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides:

$a^2 + b^2 = c^2$

Here, $x$ is the hypotenuse, and the two other sides of the triangle are 5 and $7 + 1 = 8$ units long.

Let's solve for $x$:

$5^2 + 8^2 = x^2$

$25 + 64 = x^2$

$x^2 = 89$

$x = \sqrt{89}$

Now, let's calculate the square root of 89 to find $x$.The value of $x$, rounded to the nearest tenth, is approximately $9.4$.

Would you like further clarification or additional details?

Here are 5 related questions to expand on this topic:

1. What is the Pythagorean Theorem and how is it applied?
2. How would you find the length of a missing leg if the hypotenuse and one leg are known?
3. Can the Pythagorean Theorem be used in non-right triangles?
4. What is the difference between exact answers and rounded answers in geometry?
5. How can the Pythagorean Theorem be applied in real-world situations?

Tip: Remember to check whether the triangle is a right triangle before applying the Pythagorean Theorem.